Planar Earthmover is not in L1
Assaf Naor, Gideon Schechtman
Abstract
We show that any L1 embedding of the transportation cost (a.k.a. Earthmover) metric on probability measures supported on the grid \0,1,...,n\2⊂eq 2 incurs distortion Ω( n). We also use Fourier analytic techniques to construct a simple L1 embedding of this space which has distortion O( n).
Create a lesson
Related papers
FPTAS for Polygonal Multi-Robot Motion Planning
Sayan Bandyapadhyay, William Lochet, Saket Saurabh et al.
Towards Learning-Guided Discovery of Extremal Geometric Constructions: A PatternBoost Study
Deepak Ajwani, Paula Carroll, Rishikesh Gajjala et al.
Geometric Kernel Diversity: An Axiomatic Diversity Measure in Euclidean Space
Ditbul Ban, Younghun Roh, Julian Shun et al.
Optimal Planar k Nearest Neighbors Queries for Additively Weighted Euclidean Distances and Convex Metrics
Chih-Hung Liu
The Rhythm of the Tiles: Narrow and Low Temperature Computation and Simulation in Synchronous Tile Self-Assembly
Florent Becker, Phillip Drake, Benjamin Durbin et al.
Hypergeometric Bridges for Multidimensional Grid Visibility
Ibrahim Ibrahim, Wilm Decré